Sign-up for free online course on ANSYS simulations![Problem Specification]
[1. Pre-Analysis & Start-up]
[2. Geometry]
[3. Mesh]
[4. Setup (Physics)]
[5. Solution]
[6. Results]
[7. Verification & Validation]
Problem 1
[Problem 2]
Problem 1
Problem
a) Consider the problem solved in this tutorial. At the exit of the pipe, we can define the error in the calculation of the centerline velocity as:
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\large
$$
Unknown macro: {varepsilon}
= {\mid U_c - U_
Unknown macro: {exact}
\mid}
$$
where Uc is the centerline value from FLUENT and Uexact is the exact analytical value for fully-developed laminar pipe flow. We expect the error to take the form:
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\large
$$
Unknown macro: {varepsilon}
=
Unknown macro: {K Delta r^p }
$$
where the coefficient K and the power p depend upon the method . Consider the solutions obtained on the 100x5, 100x10, and 100x20 meshes. Using MATLAB, perform a linear least squares fit of:
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\large
$$
Unknown macro: {ln varepsilon}
=
Unknown macro: {ln K + p ln Delta r}
$$
to obtain the coefficients K and p. You can look up the value of Uexact from any introductory textbook in fluid mechanics such as Fluid Mechanics by F. White. Explain why your values make sense.
b) Repeat the above exercise using the "first-order upwind" scheme for the momentum equation. Contrast the value of p obtained in this case with the previous one and explain your results briefly (2-3 sentences).
Hints
Note that the first or second order discretization applies only to the convective terms in the Navier-Stokes equations. The viscous terms are always second order accurate.
Go to [Problem 2]